Question

Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.

Answer 1

8.6

Explanation:

Distance between two points

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.`

Define the points:

• 
  `\textsf{Let}\:(x_1,y_1)=(0,0)`
• 
  `\textsf{Let}\:(x_2,y_2)=(7,5)`

Substitute the defined points into the formula:

`\implies d=√((7-0)^2+(5-0)^2)`

`\implies d=√(7^2+5^2)`

`\implies d=√(49+25)`

`\implies d=√(74)`

`\implies d=8.6\;\;\sf (nearest\: tenth)`

Therefore, the length of one of the diagonals of the rectangle is 8.6.